Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-x+3y &= 6 \\ -3x-9y &= 4\end{align*}$
Explanation: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-3x = 9y+4$ Divide both sides by $-3$ to isolate $x$ $x = {-3y - \dfrac{4}{3}}$ Substitute this expression for $x$ in the first equation. $-({-3y - \dfrac{4}{3}}) + 3y = 6$ $3y + \dfrac{4}{3} + 3y = 6$ Simplify by combining terms, then solve for $y$ $6y + \dfrac{4}{3} = 6$ $6y = \dfrac{14}{3}$ $y = \dfrac{7}{9}$ Substitute $\dfrac{7}{9}$ for $y$ in the top equation. $-x+3( \dfrac{7}{9}) = 6$ $-x+\dfrac{7}{3} = 6$ $-x = \dfrac{11}{3}$ $x = -\dfrac{11}{3}$ The solution is $\enspace x = -\dfrac{11}{3}, \enspace y = \dfrac{7}{9}$.